Enhancing the Material Balance Equation for Shale Gas Reservoirs Tyler Zymroz April 23, 2015
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Enhancing the Material Balance Equation for Shale Gas Reservoirs
Tyler Zymroz
April 23, 2015
AgendaPersonal Background
Introduction
Research1. Material Balance Equation
2. Enhancing the MBE
3. Results
Project Findings
Questions
Final Conclusion
Personal Background
Project IntroductionObjective: Increase the effectiveness of the material balance equation (MBE) for shale gas reservoirs.
– Quick and easy method to evaluate:
• Initial adsorbed gas in place, Ga
• Initial free gas in place, Gf
– Create an equation that generates a linear-line
Work FlowPerformed a
Literature Analysis
Performed a Literature Analysis
Examined Material Balance Equation practices
Examined Material Balance Equation practices
Applied current practices to data set to
identify problem
Applied current practices to data set to
identify problem
Created new method to account for desorption
Created new method to account for desorption
Tested method with data set and output
results
Tested method with data set and output
results
Material Balance Equation
The MBE is an equation based on:
– Fluid Production = Δreservoir volume due to drive mechanisms
Volumetric Gas MBE
– Underground Removal = Gas Expansion Drive
– GpBg = G(Bg-Bgi)
By replacing Bg and rearranging:
– p
Z=piZi(1-
Gp
G)
Volumetric p/Z vs. GpA graph can be generated by plotting p/Z vs. Gp.
G = Gp when p/Z = 0, therefore G = (2217/149.8) ≈ 14.8 MMMscf
y = -149.8x + 2217R² = 0.996
0
500
1000
1500
2000
2500
0 0.96 2.12 3.21 3.92
pi/
Z i(p
sia)
Cumulative Gas Produced (MMMscf)
Volumetric Gas Reservoir
p/Z vs. Gp ErrorThe p/Z vs. Gp plot is ineffective for shale res.
– Data displays linear trend initially (blue points)
– Over time data trends upward (red points)
y = -0.511x + 1705R² = 0.96621
0
200
400
600
800
1000
1200
1400
1600
1800
0 1000 2000 3000 4000 5000 6000 7000
p/Z
(p
sia)
Gp (MMscf)
OGIP Error due to Early Interpretation
Gp ≠ G
Adsorption/DesorptionAdsorption is the adhesion of gas to the face of the shale.
Desorption is the release of gas from the face of the shale.
– Deviation from trend line during the p/Z vs. Gp
– The Langmuir Isotherm
Langmuir Isotherm
Assumptions:
– Monolayer of gas on shale surface
– Equilibrium established between the free gas and adsorbed gas for a given temperature and pressure
Reasoning:
– Mathematically easy to calculate
– Desorption estimates will be conservative
Langmuir Isotherm cont.
pL
(1/2)*VL
V (p) =VL (p
p+ pL)
VL is Langmuir’s volume, max gas volume at infinite pressurepL is Langmuir’s pressure, pressure corresponding to one-half VL
V(p) is the volume of gas adsorbed per unit mass (scf/ton)
Desorption
0
50
100
150
200
250
300
350
400
0 200 400 600 800 1000 1200
Ad
sorb
ed
Gas
(sc
f/to
n)
Pressure (psi)
Gas Desorption
Gas released is equal toV(1000 - 600) = 340 - 280V(1000 - 600) = 60 scf/ton
V (pi - p) =VL (pi
pi + pL-
p
p+ pL)
Shale Gas MBEOriginal Havlena-Odeh Gas MBE
My approach:
Production terms = reservoir drive mechanisms
Desorption
Nomenclature for drives
GpBg +WpBw =G(Bg -Bgi )+GBgiSwicw + cf1- Swi
Dp
Desorption DriveEach drive mechanism = reservoir barrels (rb)
Starting point: rb (scf/ton) x ?
Reservoir bbls = desorption (scf/ton) * bulk density (ton/ft3) * bulk volume (ft3)*Gas FVF (rb/scf)
*Ga = initial adsorbed gas in place (scf)Gc = initial adsorbed gas content (scf/ton)
VL (pi
pi + pL-
p
p+ pL) 0.0312144rb
Ga0.0312144rbGc
Bg
Reservoir barrels due to desorption:
In simplified form:
Desorption Drive cont.
rb =VL (pi
pi + pL-
p
p+ pL)0.0312144rb
Ga0.0312144rbGc
Bg
rb =GaBgVLGc(pi
pi + pL-
p
p+ pL)
*Ga = initial adsorbed gas in place (scf)Gc = initial adsorbed gas content (scf/ton)
Reservoir Drive Alterations
Gas Expansion Drive
– Changed G to Gf
G(Bg-Bgi) Gf(Bg-Bgi)
Pore Compaction/Water Expansion Drive
– Changed G to Gf for water exp./pore compaction
GBgiSwicw + cf
1- SwiDp Gf Bgi
Swicw + cf
1- SwiDp
*Gf = initial free gas in place (scf)
Proposed Shale Gas MBE
Reformatted using Havlena-Odeh nomenclature:
F = (rb); net production
Eg = Bg-Bgi (rb/scf); gas expansion
Ef,w = (rb/scf); pore & water
exp.
Ed = (rb/scf); desorption
GpBg +WpBw =Gf (Bg - Bgi )+Gf BgiSwicw + cf
1- SwiDp+GaBg
VLGc(pi
pi + pL-
p
p+ pL)
GpBg +WpBw
Gf BgiSwicw + cf
1- SwiDp
BgVLGc(pi
pi + pL-
p
p+ pL)
Proposed Shale Gas MBE cont.
The equation can be rewritten in the format:
F = GfEg + GfEf,w + GaEd
Simplified
F = Gf(Eg+Ef,w) +GaEd
Dividing (Eg+Ef,w) to create:
F
Eg +Ef ,w=Ga (
EdEg +Ef ,w
)+Gf
A straight line can be generated by graphing:
vs.
Straight Line Interpretation
F
Eg +Ef ,w(
EdEg +Ef ,w
)
F /(
E g+
E f,w
) sc
f
Ed/(Eg + Ef,w) unitless
m = Ga
b = Gf
y = mx + b
Coal Bed Methane Analogy
Assumptions:
– Similar Reservoir drive mechanisms
– Geological characteristics not a factor
– High water production does not affect analysis
Desorption is present in both reservoirs!
Example Plot Using CBM data
• Graph: Ga = 12,657 MMscf and Gf = 69,243 Mscf• Volumetric: Ga = 12,763 MMscf and Gf = 37,189 Mscf
y = 12,657,083,257.54x + 69,243,440.46R² = 1.00
0
500000000
1E+09
1.5E+09
2E+09
2.5E+09
3E+09
3.5E+09
4E+09
4.5E+09
5E+09
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
F/(E
g+E f,
w)
(scf
)
Ed/(Eg+Ef,w)
Plot Using CBM Data
Project FindingsResults
• Created MBE analysis
• Was not able to estimate Gf
• Method appropriate for dry and wet gas
• Increase accuracy of reserve estimates
Recommendations• Apply method to
Marcellus/Utica dry or wet gas reservoir
• Determine effect of pore compaction/water expansion drive for shale reservoirs
• Attempt to Generate adsorption isotherm
Questions?
ConclusionMaterial Balance Equation
Errors Associated with p/Z method
Adsorption/Desorption
New method to estimate reserves
Recommendations for moving forward
Thank You!
Rearranging for p/ZInitial: GpBg = G(Bg-Bgi)
Gp = G (Bg-Bgi)/Bg
Substitute:
Gp = G - GpZi/(piZ)
Multiply Each side by pi/Zi
Gppi/Zi =Gpi/Zi – Gp/Z
Gp/Z = pi/Zi(G-Gp)
Divide out G
p/Z = pi/Zi(1-Gp/G)
Final:
Bg = 0.02827TZ
p
p
Z=piZi(1-
Gp
G)
Approximating Langmuir Volume and Pressure
y = -307.21x + 521.78 R² = 0.99981
0
100
200
300
400
500
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Me
than
e A
dso
rpo
n (
scf/
ton
)
V/p (Adsorbed Methane per Pressure, scf/ton/psia)
VL and pL Approxima on
y = -307.21x + 521.78 R² = 0.99981
0
100
200
300
400
500
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Me
than
e A
dso
rpo
n (
scf/
ton
)
V/p (Adsorbed Methane per Pressure, scf/ton/psia)
VL and pL Approxima on
VL = b = 521.78 scf/tonpL = -m = 307.21 psia
Bulk Volume Calculation
Start: Ga= 1359.7AhρbGc
Where
CF = 0.0312144 (ton/ft3) per (g/cc)
Gc = initial adsorbed gas content (scf/ton)
ρb = bulk density (g/cc)
1359.7 = 43560*0.0312144
End: 43560Ah (ft3) = Ga/(0.0312144ρbGc)
BET Isotherm
• Mathematical equation:
V (p) =
VmonoC(p
po)
(1-p
po)(1+C(
p
po)-p
po)
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